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Man and Beast 18: Complex Pieces with Simple Ratios

MAB 03: From Ungulates Outward describes how, for any two distinct square-board oblique leapers with prime Square Of Leap Length (SOLL), another two distinct oblique leapers have a SOLL which is their product. If one prime-SOLL piece is instead radial (the Ferz) a single piece, the oblique piece's dual and suffixed -mel after the Camel, has twice the oblique piece's SOLL. Conversely a single prime-SOLL oblique piece has an oblique and a radial piece with the square of its SOLL. To the simple pieces it adds compounds of two duals, compounds of two pieces sharing a product SOLL such as the Bat of John Savard's Leaping Bat Chess, and crossover compounds of one piece with a given product SOLL and the other's dual.

MAB 05: Punning by Numbers adds cubic-specific leapers sharing SOLLs of either each other or square-cell ones, as well as pairs of semi-duals with a SOLL ratio of 2, MAB 14: Oddly Oblique 2d and 3d hex ones likewise. Compounds of semi-duals use the same endings as those of duals. From compounds' common sets of endings MAB 07: When Beasts Collide derives part-symmetric and mixed-range oblique pieces. The article immediately before this includes a compound of two radial pieces of SOLL 4, the Twoleaper.

This article adds compounds of two oblique pieces sharing a SOLL, and with SOLLs in simple ratios, beyond the MAB 03 and 05 examples. Recurring sets of endings make for some desperate names including meteor types (µ), types of Classical nymph (ñ), and adjectives (æ unless also a noun). As ever I am open to better ideas.

The acknowledgments, overview, and glossary to the series can be found here. Established pieces have a link to their Piececlopedia page. The images used in this series, and indeed in most of my pages, can be found here.


Compounds with or between MAB 05 pieces may be inevitable or coincidental.

A leaper whose coordinates are 5 and another nonzero number may share an odd SOLL with one whose coordinates are 4, 3, and the same other number. 29 (4:3:2 Rytas, 5:2:0 Satyr) and 58 (7:3:0 Samel) adds to the Sadhu Rytas+Satyr=STARRINESS, Rytas+Samel=SAMIZDAT and to the Vandyman Eniv+Vine=NAIAD ñ, Eniv+Vump=BOOZEUP. For 41 (4:4:3 Rotcer, 5:4:0 Rector, 6:2:1 Dancer) and 82 (9:1:0 Remel and 8:3:3 Rootler) the 5 simple symmetric pieces have 10 symmetric compounds, so I reuse other MAB 03 endings. This adds to the Reseau and Rondeau Rotcer+Rector=REDRESS, Rotcer+Dancer=DARWIN, Rector+Dancer=DEMOISELLE (French for damsel), Rector+Rootler=RHEOSTAT, Rotcer+Remel=CORHEOSTAT, Dancer+Rootler=ROOTOUT, Dancer+Remel=REDACTION, Rootler+Remel=COREDRESS. To the Uandyman and Talisman it adds UNIDAD (Spanish for unity), GAVIAL (an Asian crocodile), AUDITOR, UPANDUP, COUPANDUP, TARGET, AUDACE (French for audacity), and COUNIDAD. 61 (6:4:3 Nosrap, 6:5:0 Parson) and 122 (11:1:0 Pamel, 8:7:3 Onlooker) adds to the Parvenu and Nosferatu Nosrap+Parson=NOSINESS, Parson+Onlooker=PRAYERMAT, Nosrap+Pamel=COPRAYERMAT, Onlooker+Pamel=CONOSINESS. To the Nandyman and Estonian it adds NOMAD, TURNUP, COTURNUP, CONOMAD. 89 (7:6:2 Fruitbat, 8:4:3 Emonorga, 8:5:0 Agronome) and 178 (13:3:0 Gamel) cheats based on the unlikelihood of a xyrixa board big enough to have duals of the Fruitbat and Emonorga. This adds to the Gateau Fruitbat+Emonorga=COGATEAU, Fruitbat+Agronome=GEOSTAT, Emonorga+Agronome=EAGERNESS, Fruitbat+Gamel=COEAGERNESS, Emonorga+Gamel=COGEOSTAT. To the Iandyman it adds COIANDYMAN, GETUP, RINGROAD, CORINGROAD, COGETUP.

A leaper whose coordinates are 5 and another nonzero number may share an even SOLL with one whose coordinates are 4, 3, and the same other number. 13 (3:2:0 Zebra) and 26 (4:3:1 Arbez, 5:1:0 Zemel) adds to the Zebu Zebra+Arbez=ACROBAT, Arbez+Zemel=AIRINESS and to the Sandyman Epirts+Stripe=SPLITUP, Epirts+Sump=SLIPROAD. 17 (3:2:2 Fencer, 4:1:0 Giraffe) and 34 (4:3:3 Effarig, 5:3:0 Gimel) adds to the Guru and Feu Fencer+Giraffe=TOPHAT, Giraffe+Effarig=LOFTINESS, Fencer+Gimel=COLOFTINESS, Effarig+Gimel=COTOPHAT. To the Bandyman and Fisherman it adds LIFTUP, DRYAD ñ, CODRYAD, COLIFTUP. 37 (6:1:0 Flamingo) and 74 (7:4:3 Ognimalf, 7:5 Famel, 8:3:1 Octodont) has both this connection and the 7:4-8:1 one, so I add further sets of endings. Thus it adds to the Flambeau Flamingo+Ognimalf=OGRESS, Flamingo+Octodont=FRIGID æ, Ognimalf+Famel=OFFBEAT æ, Ognimalf+Octodont=OCEANUS (a mythical Titan), Famel+Octodont=OCELOT. To the Mandyman it adds HAMMERHEAD, JAMMING, TEACUP, GYMNAST, JETTY.

Coordinates 5:5 and 7:1 also yield shared SOLLs. 27 (5:1:1 Exorcist) and 54 (5:5:2 Expounder, 7:2:1 Propounder) adds to the Xanadu Exorcist+Propounder=PREHEAT, Expounder+Propounder=EXPRESS and to the Statesman Stake+Rant=STIRRUP, Tale+Rant=RAILHEAD. 43 (5:3:3 Fieldmouse) and 86 (6:5:5 Flittermouse, 7:6:1 Pipistrelle) adds to the Fichu Fieldmouse+Pipistrelle=MOUSINESS, Flittermouse+Pipistrelle=OPERAHAT and to the Macedonian Meadow+Pipsqueak=PINHEAD, Aria+Pipsqueak=PICKUP. 51 (5:5:1 Feaster, 7:1:1 Slimmer) and 102 (7:7:2 Skimmer) adds to the Shiatsu Feaster+Slimmer=FASTNESS (a fortification), Feaster+Skimmer=FERMAT (name of a famous mathematician) and to the Linesman Girth+Lank=GALAHAD, Girth+Film=GRINDUP. 59 gives 5:5:3 Broadwayman + 7:3:1 Highwayman = THREAT and Breadth+Height=HOLDUP. 99 gives 7:5:5 Whinger + 7:7:1 Lounger = VISHNU and Inlet+Outlet=THESPIAN - as the Lounger and Whinger have no duals on any size of 3d board that I am considering, I treat them as duals to simplify naming their other compounds.

25 and 50 fit neither pattern as 5:5:0 is radial but there are of course the 4:3:0 Antelope and 7:1:0 Namel to go with the 5:4:3 Epoletna. These add to the Anu Antelope+Epoletna=AUTOCRAT. Epoletna+Namel=ENDLESS æ and to the Headman Haste+Etsah=PUNCHUP (punning on the drink punch, named after its 5 ingredients), Etsah+Hardness=TESTPAD. 33 (4:4:1 Wideplayer, 5:2:2 Longplayer) and 66 (5:5:4 Loremaster, 7:4:1 Viremaster, 8:1:1 Wiremaster) are a more complex set involving both 5:5-7:1 and 7:4-8:1 connections, so Viremaster compounds reuse the endings of Octodont ones plus an extra pair. This adds to the Lowenbrau and Winthru Wideplayer+Longplayer=PLAYFULNESS, Wideplayer+Loremaster=BACKBEAT, Wideplayer+Viremaster=VINDICTIVE æ, Longplayer+Viremaster=VIRGINID µ, Longplayer+Wiremaster=COBACKBEAT, Loremaster+Viremaster=VIEWINGSPOT, Loremaster+Wiremaster=COPLAYFULNESS, Viremaster+Wiremaster=VIGOROUS æ. To the Locrian and Witan it adds POWERLEAD, KNEESUP, THERAPIST, THRILLING, COKNEESUP, THIRSTY æ, COPOWERLEAD, and THROWPAST.

Other 7:4-8:1 connections yield such compounds. 45 (5:4:2 Chipmunk) and 90 (7:5:4 Clinger, 8:5:1 Hogger) adds to the Ciseau Chipmunk+Hogger=CHEAT, Clinger+Hogger=CHOPPINESS and to the Chippan CHINUP, GREYHEAD (person whose hair has gone grey). 69 (7:4:2 Gerbil, 8:2:1 Muskrat) and 138 (8:7:5 Muddler) add to the Milieu Gerbil+Muskrat=GESHMAT (Yiddish for an apostate from Judaism), Gerbil+Muddler=GRIMINESS and to the Mauretanian MARKUP, INROAD. 81 (7:4:4 Oppossum, 8:4:1 Ultimatum) and 162 (8:7:7 Lumel) add to the Uluru Opossum+Ultimatum=UPBEAT, Opossum+Lumel=LOOPINESS and to the Deadman SOBERUP, SPREAD.

I have yet to deal much here with the link between 10 and 8:6, but for SOLLs 101 (10:1 Macaw, 8:6:1 Wacam, 7:6:4 Examiner) and 202 (11:9 Mamel) I again use the unlikelihood of a xyrixa board big enough for Wacam and Examiner duals to treat the pair like duals. To the Marabou this adds Macaw+Wacam=MATTRESS, Macaw+Examiner=MANXCAT, Wacam+Examiner=COMARABOU, Wacam+Mamel=COMANXCAT, Examiner+Mamel=COMATTRESS. To the Wandyman it adds WORKLOAD, WARMUP, COWANDYMAN, COWARMUP, and COWORKLOAD.

That leaves coincidentally-shared SOLLs. 19 (3:3:1 Underscore) and 38 (5:3:2 Sustainer, 6:1:1 Nurturer) adds to the Nunchaku Underscore+Sustainer=SUNHAT, Nurturer+Sustainer=TAUTNESS and to the Cracksman Cedilla+Subordinate=RISEUP, Runaround+Subordinate=ROUNDHEAD. 62 gives 6:5:1 Endower + 7:3:2 Avower = VAGUENESS and Rite+Fate=DREAD. 53 (6:4:1 Midwife, 7:2:0 Stork) and 106 (9:5:0 Somel) adds to the Sou Midwife+Stork=BROODINESS, Midwife+Somel=FEAT and to the Gandyman Birth+Gift=NAVIDAD (Spanish for nativity), Birth+Gump=REARUP. 57 (5:4:4 Numbat, 7:2:2 Wombat) and 114 (7:7:4 Worrier, 8:5:5 Tinkerer, 8:7:1 Beggar) adds to the Wouwou and Tinamou Wombat+Numbat=TWOMBAT (my own coinage), Numbat+Worrier=NUTTINESS, Wombat+Tinkerer=CONUTTINESS, Wombat+Beggar=WORSEN (a verb), Numbat+Beggar=NOUVELLE (French for a news item), Worrier+Tinkerer=COTWOMBAT, Worrier+Beggar=TINCTURE, Tinkerer+Beggar=TITRATION. To the Moravian and Mondrian it adds DOUBLEUP, MUTTONHEAD (a kind of idiot), COMUTTONHEAD, MODULAR æ, MASTICATOR, CODOUBLEUP, DOWNHILL æ, DEFACE (a verb). Finally 73 (6:6:1 Hamster, 8:3:0 Huckster) and 146 (11:5:0 Humel) adds to the Hutu Hamster+Huckster=HAMMINESS, Hamster+Humel=HABITAT and to the Tandyman Fray+Tray=FOOTPAD, Fray+Tump=FRAMEUP.

Any compound of two odd-SOLL pieces is again colourswitching, one of two even-SOLL pieces colourbound and unswitching, and a mixed-SOLL compound (on a large enough board) unrestricted. If both SOLLs divide by 4 with remainder 3 it shares their binding, which is more familiar as the Unicorn's. It still switches between Bishop bindings. A compound of leapers with remainders 2 and 3 is unbound for the same reason as the Governor (Bishop+Unicorn).


As expected, adding the suffix -rider to the first five letters of the compound of two simple leapers or, where it is used, to the Co- prefix and the five letters after that gives the compound of the simple leapers' riders. Thus Rytasrider+Satyrrider=STARRRIDER, Zebrarider+Arbezrider=ACROBRIDER, Striprider+Epirtrider=SPLITRIDER, Birthrider+Giftrider=BROODRIDER (unambiguous as MAB 14's Brood is already partly long-range), et cetera.

Likewise Curved and Crooked compound riders exist. 3d Curved compounds are limited pretty much to Bezra+Abrez=ARCOBAT and Mezel+Abrez=RIAINESS. Crooked compounds include Longzebraflyer+Longarbezflyer=LONGACROBFLYER, Shortsatyrsidler+Shortrytassidler=SHORTSTARRSIDLER, and many others. This page's compound pieces also allow easy EMD definitions for a further group of Crooked pieces. Just as the -duellers of MAB 09: Mighty Lika a Rose alternate moves of one piece at right angles to give its dual's EMD, so -TRIALLERS alternate moves of a pair of semi-duals to give a hypotenuse piece EMD. For example the ELFTRIALLER's EMD is Playfulnesswise, the FENCETRIALLER's Burgesswise, the UNDERTRIALLER's Twombatwise, and the LECTUTRIALLER's Coplayfulnesswise. Given that the NINJATRIALLER alternates actual duals it is unsurprising that it is an exception with a part-radial Xeprechaunwise EMD.

By now you may be wondering why, when only two simple pieces share a SOLL, I do not just insert the SOLL into Root...leaper (and for multiple leaps Root...rider). Firstly the pieces above combine only rectilinear leapers, and might not exhaust the SOLL for other geometries. Secondly Root...leaper does not lend itself to naming part-symmetric and mixed-range pieces. Part-symmetric ones include Arbez+Stripe=ARBUP, Zebra+Epirts=ZEBUP, Arbez+Sump=ARBAD, Zemel+Epirts=ZEMAD. Giraffe+Foil=GIRUP, Giraffe+Hctolb=GIRAD, Fencer+Blotch=FENUP, Fencer+Bump=FENAD, Effarig+Blotch=EFFAD. Mixed-range ones include Zebrarider+Arbez=ZEBRARAT, Arbezrider+Zebra=ARBEZRAT, Striprider+Epirts=STRIPRUP, Epirtrider+Stripe=EPIRTRUP.

Where Root...leaper names makes sense is for compounds of three or more simple leapers. Thus Rotcer+Rector+Dancer is indeed ROOTFORTYONELEAPER - or ROOTFOURTYONELEAPER for determined spelling reformers - Ox+Bittern+Molerat (on a cubic board) ROOTSIXTYFIVELEAPER, all three masters ROOTSIXTYSIXLEAPER, Famel+Ognimalf+Octodont ROOTSEVENTYFOURLEAPER, Agronome+Fruitbat+Emonorga ROOTEIGHTYNINELEAPER, Macaw+Examiner+Wacam ROOTHUNDREDANDONELEAPER, and Worrier+Tinkerer+Beggar ROOTHUNDEREDANDFOURTEENLEAPER. This is my first mention of the Molerat, and no wonder, as it is a fifth simple piece in the SOLL 65/130 group. Its compounds with the other four reuse the endings of Viremaster compounds. Thus Molerat+Ox=MORPHEUS, Molerat+Bittern=PARROT, Molerat+Bimel=MORBID æ, Molerat+Zomel=MOTIVE, Loomer+Labour=HOLDFAST (as one might do to one's labours), Loomer+Pond=AVIARY, Loomer+Pump=PULLING, Loomer+Lump=LOCALIST.

SOLLs dividing exactly by 9 often add non-coprime components such as Chipmunk+Chamois (45), Expounder+Propounder+Sessowary (54), Clinger+Hogger+Cassowary (90), Whinger+Lounger+Letdown (99), and Bystander+Zhemois (117). Likewise with 25 Quail+Liamniahc+Chainmail is ROOTHUNDREDANDTWENTYFIVELEAPER. To the short-range -leaper and long-range -rider suffix, are added -ROVER extending just the coprime component(s) -BANTE just the twice-coprime, -TRANTE just the thrice-coprime, et cetera. Note that this still gives no name for, for example, the Expounder+Sessowary compound, whose directions form the EMD of the NIMELTRIALLER.


In MAB 05 two sets of compounds with SOLL ratios of 1½, 3, and/or 6 have the -elle/-on/-or/-ace endings. This will not do as a general rule, as the next obvious set of such pieces use some of the same SOLLs: 9 (2:2:1 Ninja) and 18 (4:1:1 Nimel). These use the same endings as the Molerat compounds. Ratios with 27 and 54 give Ninja+Exorcist=INCISIVE æ and Nimel+Exorcist=NIMBUS, duals Ninja+Expounder=CONIMBUS and Nimel+Expounder=COINCISIVE æ, and further compounds Ninja+Propounder=NEREID ñ and Nimel+Propounder=DESPOT. FO versions are DEIST/DOWNCAST/CODOWNCAST/CODEIST/CHANGELING/TYRANNY.

5/10/30 is perhaps easy to overlook, as no cubic piece has the SOLL 15 to match the 5:2:1 Monk's 30. This gives Knight+Monk=PATRIOT and Camel+Monk=CYGNID µ. Likewise a lack of SOLL-39 cubic pieces masks the 13/26/39/78 group. This gives Zebra/Arbez/Zemel compounds with the 7:5:2 Bandicoot which I term the ZEALOT/ABRASIVE/ZETOID. FO versions are ARMOURY/WRAPPING and SEVERITY/ENIGMATIST/STRING.

11/22/33/66 is a very full group. Compounds with longest SOLL 33 - carefully named to avoid clashes with previous 33/66 compounds - are Elf+Wideplayer=POLYGLOT, Elf+Longplayer=FOCUS, Lecturer+Wideplayer=LEONID µ, Lecturer+Longplayer=INFORMATIVE æ. Duals are Elf+Loremaster=COINFORMATIVE, Elf+Wiremaster=COLEONID, Lecturer+Loremaster=COFOCUS, Lecturer+Wiremaster=COPOLYGLOT. Viremaster compounds reuse MAB 03 endings with Elf+Viremaster=VILLANELLE (a kind of poem), Lecturer+Viremaster=VISION. FO versions are CRONY/CONTRAST/LOWERING/LEFTIST, COLEFTIST/COHIRING/COCONTRAST/COCRONY, and THYRISTOR/THINFACE.

30/45/90 gives Monk+Chipmunk=RECLUSIVE æ, Monk+Clinger=AMBIGUOUS æ (from the contrast between its components' names). FO versions are MINIMALIST/OUTCAST.

17/34/51/102 gives Fencer+Feaster=FERROUS æ, Giraffe+Feaster=BIGSHOT, Fencer+Slimmer=HOTSHOT, Giraffe+Slimmer=GERONTIUS, Effarig+Feaster=FESTIVE æ, Gimel+Feaster=GEMINID µ, Effarig+Slimmer=SOLENOID, Gimel+Slimmer=GENITIVE æ. Duals are Fencer+Skimmer=COSOLENOID, Giraffe+Skimmer=COGENITIVE, Effarig+Skimmer=COHOTSHOT, Gimel+Skimmer=COGERONTIUS. FO versions are TYPECAST/TUBBY/SKINNY/BALLAST all but last æ, FATALIST/SITTING/LASHING/HELLENIST, and COLASHING/COHELLENIST/COSKINNY/COBALLAST.

19/38/57/114 gives Underscore+Numbat=NUCLEUS, Underscore+Wombat=UPSHOT, Nurturer+Numbat=NARRATIVE, Sustainer+Numbat=SELEUCID (a dynasty of Greek rulers of Syria), Nurturer+Wombat=NURSEMAID, Sustainer+Wombat=SUBVERSIVE. Duals are Underscore+Worrier=CONURSEMAID, Underscore+Tinkerer=CONARRATIVE, Nurturer+Worrier=COUPSHOT, Nurturer+Tinkerer=CONUCLEUS. Sustainer compounds are Sustainer+Worrier=THESAURUS and Sustainer+Tinkerer=STEWPOT. FO versions are BLAST/MOCKERY/MURALIST/MUSING/RUNNING/MORALIST, CORUNNING/COMURALIST/COMOCKERY/COBLAST, and ENTHUSIAST/SUBWAY.

46/69/138 reuses Opossum-compound endings for Gerbil/Muskrat/Muddler plus 6:3:1 Genome as GENEPOOL, GNOMON, GEMELLE æ (for pairs of narrow bands in heraldry). 25/50/75 gives Antelope/Namel/Epoletna plus 7:5:1 Petmouse as PENSIVE, PENTELICUS (a Greek mountain), PEPPERPOT. FO versions are CRITIC/GRIMACE/MORDOR, THANATOLOGIST (one who stydies death)/ICONOCLAST/TETCHY æ.

Among 27/54/81/162 pieces, Opossum compounds reuse -elle/-on plus an extra pair to give Exorcist+Opossum=ECHELON (an upper layer of a career structure), Expounder+Opossum=ESTELLE (word in one form of old French for star), Propounder+Opossum=PROTOCOL. The rest reuse -ive/-ot/-us/-id with Exorcist+Ultimatum=ENTREPOT, Expounder+Ultimatum=ELLIPSOID, Propounder+Ultimatum=PROGRESSIVE, Exorcist+Lumel=COELLIPSOID, Expounder+Lumel=COENTEPOT, Propounder+Lumel=PROTEUS. FO versions are SURFACE/TRAITOR/RUSTIC and TRENDY/RAIDING/PURIST/CORAIDING/COTRENDY/RADAGAST. The last is a Tolkien character's name.

62/93 gives Endower/Avower plus 8:5:2 Vacillator as ENTMOOT (a meeting of Tolkien's Ents), VACUOUS æ. FO versions are FAIRWAY/FLABBERGHAST (a verb meaning to amaze and shock).

33/66/99 reuses MAB 05 endings with Wideplayer+Whinger=WINGNUT, Longplayer+Lounger=LEQUELLE (French relative pronoun), Loremaster+Lounger=LAOMEDON (a Greek hero), Wiremaster+Whinger=WITTGENSTEIN (a famous philosopher). Treating the Lounger and Whinger as duals extends to Wideplayer+Lounger=COWITTGENSTEIN, Longplayer+Whinger=COLAOMEDON, Loremaster+Whinger=COLEQUELLE, Wiremaster+Lounger=COWINGNUT. Viremaster compounds follow a triangle with Vishnu, with each compound using the opening letters of the absent piece of the three: Viremaster+Whinger=LOVELESS æ, Viremaster+Lounger=WHINCHAT (a bird). FO versions are WIDGET/LOCATOR/OUTRACE/INTERVAL, COINTERVAL/COOUTRACE/COLOCATOR/COWIDGET, OVERLOAD/ICEUP.

35/70/105 gives the compounds with Oddfellow/Dormouse plus 8:5:4 Dodderer as ODYSSEUS and ADDITIVE. 78/117 gives Bandicoot plus 8:7:2 Bystander as BABOON. 41/82/123 gives Rotcer/Rector/Dancer/Rootler/Remel plus 7:7:5 Roper as RHOMBOID, RECURSIVE æ, DATAPOOL, ROBOT, and RELIGIOUS (mostly æ). 43/86/129 gives Fieldmouse+Filcher=FLORID æ, Fieldmouse+Pilferer=FYLFOT (a less contentious name for the swastika), Pipistrelle+Filcher=PITEOUS, Pipistrelle+Pilferer=FIXATIVE. Treating the Filcher and Pilferer as duals in the absence of the real ones gives Flittermouse+Filcher=COFYLFOT, Flittermouse+Pilferer=COFLORID. FO versions are STANDFAST/SHORTLIST, NECKLACE, ALLUDING æ/UNIONIST (various types of politician)/GRAMMATIC æ/TOURNEY (a type of jousting)/UNCAST æ (of dramatic characters yet to be assigned an actor), and FRAMING/MERCENARY/FLYPAST/PRESERVATIONIST/COMERCENRARY/COFRAMING.

51/102/153 gives Feaster+Shirker=SYMBOL, Slimmer+Shirker=SEYCHELLE (any one island of the Seychelles archipelago), and Skimmer+Shirker=STASIMON (part of an ancient Greek drama). FO versions are GASTRIC/LAMINATOR/FIREPLACE.


Dual or dual-named hex compounds follow the MAB 14 rule that the hex-specific compound takes the Co- prefix. Aurochs plus Zebra/Zemel are COAIRINESS/COACROBAT, Mountie plus Knight/Camel/Chipmunk/Clinger COCYGNID/COPATRIOT/COAMBIGUOUS/CORECLUSIVE, Student plus Underscore/Nurturer/Numbat/Wombat/Worrier/Tinkerer COTAUTNESS/COSUNHAT/COSTEWPOT/COTHESAURUS/COSUBVERSIVE/COSELEUCID, Germinator plus Muskrat/Muddler COGEMELLE/COGNOMON, Pentagram plus Antelope/Namel COENDLESS/COAUTOCRAT, Opportunist plus Ninja/Nimel/Exorcist/Expounder/Ultimatum/Lumel CODESPOT/CONEREID/COEXPRESS/COPREHEAT/COPROTEUS/COPROGRESSIVE, Newlywed plus Vampire=COVAGUENESS, Videoplayer plus Elf/Lecturer/Wideplayer/Longplayer/Loremaster/Wiremaster/Lounger/Whinger COVISION/COVILLANELLE/COVIGOROUS/COVIEWINGSPOT/COVIRGINID/COVINDICTIVE/COLOVELESS/COWHINCHAT, Goose plus Flamingo/Famel COOFFBEAT/COOGRESS, Cormorant plus Flamingo/Goose/Famel COOCELOT/COOCEANUS/COFRIGID, Barnowl plus Aurochs/Zebra/Zemel COABRASIVE/COZETOID/COZEALOT, Prizemouse plus Fieldmouse/Flittermouse COOPERAHAT/COMOUSINESS, Housemouse plus Chipmunk/Clinger COCHOPPINESS/COCHEAT, Bettong plus Wombat/Numbat/Worrier/Tinkerer COTINCTURE/COTITRATION/COWORSEN/CONOUVELLE, Rhymer plus Satyr/Samel COSAMIZDAT/COSTARRINESS, Dallier plus Rotcer/Rector/Rootler/Remel COROOTOUT/COREDACTION/CODARWIN/CODEMOISELLE. Likewise with FO pieces.

Hex-prism boards unite dual-named pieces such as Foal+Fortnight=FROUFROU, Student+Sustainer=SUSU (a species of river dolphin), Tutor+Tucotuco=TUTU, Germinator+Genome=GENOU (French for knee, soft G), Hybridiser+Hylonome=HAIKU (see my variant Haiku Shogi), Pentagram+Epoletna=PENDU (French for a hanged man), Rytas+Rhymer=RYUKYU (a Japanese archipelago), Newlywed+Endower=NEHRU, Vampire+Avower=VANUATU, Goose+Ognimalf=GLORIEU (French for glorious). FO versions - former nationalities unless commented in brackets - are FORTRAN (a programming language), POSTMAN (plural POSTMEN), RURITANIAN (an imaginary nationality), SECTARIAN (opposite of Ecumenist), HIBERNIAN, PELICAN (a bird with heraldic associations), VENETIAN, BESTMAN (plural BESTMEN, a man delivering a ring at a rite), HANGMAN (plural HANGMEN, a position that some view as macabre), TEGEAN.

The Cotautness, Covagueness, Cooceanus, Cooperahat, and Cotitration have the special signifiance of being the compound of a pure-hex piece and its hex-prism 90° rotation around the nonstandard diagonal. Other compounds with this property are Sennight+Foal=HORSINESS, Aurochs+Baker=BARMAID, Overscore+Offscore=OPENNESS, Heptagram+Sceptic=HOMELINESS, Guineapig+Gopher=GOAT, and their FO forms OFFROAD æ/OPENING/CENTAD (group of a hundred)/SOCIEDAD (Spanish for society, C pron. th)/PINUP. Also associated with the Horsiness and Openness are Sennight+Fortnight=SHABBAT (sabbath in original language), Sennight+Overscore=SEDATIVE, Sennight+Offscore=SENGAZELLE, Foal+Offscore=OFFENSIVE, Fortnight+Offscore=OFFICIOUS æ, Sennight+Votary=SEDITIOUS æ, and their FO forms SEXIST/SENVISOR/RACIST/FORECAST/STEADFAST æ. Also associated with the Barmaid are Zebra+Baker=BEEHIVE, Baker+Zemel=BACCHUS, Baker+Barnowl=BAGATELLE, and their FO forms OBOEIST/ORGIAST/OVIPOSITOR. Also associated with the Covagueness are Newlywed+Avower=LOVEBOAT, Vampire+Endower=COLOVEBOAT, Newlywed+Vacillator=BRIDESMAID, Vampire+Vacillator=EVASIVE, and their FO forms DIALUP/CODIALUP/FAIRING (an engineering term)/FASCIST. Also associated with the Cooceanus are Cormorant+Ognimalf=COGNITIVE æ and its FO form CELLIST. Also associated with the Cooperahat are Fieldmouse+Woodmouse=FICTITIOUS, Prizemouse+Woodmouse=WHATNOT, Woodmouse+Flittermouse=FIXATIVE, and their FO forms METCAST (short for meteorogical forecast)/DOWRY/DOGMATIST. Also associated with the Homeliness are Sceptic+Hemel=HEIMAT and its FO form DOLLINGUP. Also associated with the Goat are Guineapig+Agouti=AGAPANTHUS, Gopher+Agouti=GALIOT (a kind of ship), Guineapig+Marmot=MAGINOT (a famous line of fortifications), Gopher+Marmot=GRAMPUS (a sea monster), Agouti+Marmot=MAGNIFICAT (a kind of hymn), Gopher+Grumbler=GORMLESS æ, Agouti+Grumbler=AGGRESSIVE æ, Marmot+Grumbler=MAGGID (a Jewish wise man), and their FO forms GASBLAST/PODGY æ/PRECAST æ/RAUNCHY æ/GANGUP/POTHEAD (a cannabis addict)/GRAPHOLOGIST/RIGGING.

Among SOLLs not associated with singly-oblique hex-prism pieces 10/20 adds Camel+Calibrator=CARESS. 11/22/44 adds to the Lefanu and Tutu Elf+Tutor=RETREAT, Lecturer+Tutor=LETTERPRESS, Elf+Tucotuco=COLETTERPRESS, Lecturer+Tucotuco=CORETREAT. In Lewis Carroll's Pig Tale, "letterpress, when toasted, loses its good looks". 23/46 adds to the Genou and Haiku Germinator+Hybridiser=GREATCOAT, Hybridiser+Genome=GHASTLINESS, Germinator+Hylonome=COGHASTLINESS, Genome+Hylonome=COGREATCOAT. 25/50/75 adds Pentagram+Petmouse=PANTRYMAID, Antelope+Anomalure=ANEROID (a kind of barometer), Pentagram+Anomalure=ARCHIVE, Namel+Anomalure=ANKLEBOOT, and Petmouse+Anomalure=PANAMAHAT. 29/58 adds to the Sadhu, Ryuku, (Co-)Samuzdat, and (Co-)Starriness Satyr+Travesty=STAID æ, Rytas+Travesty=TRANSITIVE æ, Travesty+Samel=TALIPOT (a kind of palm tree), Travesty+Rhymer=TREMENDOUS æ. 35/70 adds to the Dropthru Oddfellow+Fanatic=MADNESS and Fanatic+Dormouse=DOORMAT. 49/98 adds to the Eheu/Homeliness Sceptic+Hemel=HEIMAT. For 53/106 I note the lack of a second SOLL 106 piece and treat Drynurse and Wetnurse as duals to give Stork+Wetnurse=WASHPOT, Midwife+Wetnurse=AQUEOUS æ, Stork+Drynurse=DRACONID µ, Midwife+Drynurse=DERIVATIVE, Wetnurse+Drynurse=COSOU, Wetnurse+Somel=CODRACONID, Drynurse+Somel=COWASHPOT. 55 gives Tesselator+Divider=DIPLOMAT. FO versions are FEETUP, HAMADRYAD ñ, CLAMUP/OREAD ñ/COOREAD/COCLAMUP, PILEUP/CASELOAD/COCASELOAD/COPILEUP, TAPPING/QUICKENING/MONOPOLIST/MONODY (a kind of chant)/TEAMUP, DEALING/DENTIST/DELIVERY/DIECAST, QUITEMAD/RESTUP, WEEDY æ/WESTCOAST (the rainier coast of European countries)/DRAINING/DRAMATIST/COGANDYMAN/CODRAINING/COWEEDY, and MASHUP. There is no ambiguity in the meaning of BRIDERIDER and MAGNIRIDER as riders of the Bridesmaid and Magnificat as MAB 06's Bride and Magnifier are already partly long-range.

Some compounds with SOLL ratio 1 or 2 require additional endings, which I have yet to devise; help is welcome. Such pieces combine Golem/Spectre/Wraith with Fortnight, Bustard/Gull with Flamingo/Goose/Cormorant/Famel, and Boneshaker with Nurturer/Sustainer. As the Molerat and Hystrix have no duals on any size of 3d board that I am considering, Hystrix plus Ox/Bittern/Bimel/Xomel can be COMOTIVE, COMORBID, COPARROT, and COMORPHEUS, likewise FO pieces.

Xyrixa and hex-prism compounds of all pieces sharing a leap length often have many components. The ROOTTHIRTYSEVENLEAPER is Flamingo+Goose+Cormorant on a xyrixa board but Flamingo+Goose+Bustard+Cormorant+Gull on a hex-prism one. Fieldmouse+Prizemouse+Woodmouse is ROOTFORTYTHREELEAPER on both. On xyrixa boards the ROOTTHIRTYTHREELEAPER unites Long-, Wide-, and Video-players while Remel+Rootler+Dallier is ROOTEIGHTYTWOLEAPER. On hex-prism boards Zebra+Aurochs+Baker is ROOTTHIRTEENLEAPER, Satyr+Rytas+Travesty ROOTTWENTYNINELEAPER, Stork+Midwife+Wetnurse+Drynurse ROOTFIFTYTHREELEAPER, Numbat+Wombat+Bettong ROOTFIFTYSEVENLEAPER, and Ox+Bittern+Molerat+Hystrix ROOTSIXTYFIVELEAPER. SOLLs dividing exactly by 4 often mix in non-coprime components such as Calibrator+Charolais (20), Golem+Spectre+Wraith+Semming+Fomming (28), Tawnyowl+Snowyowl+Crane (40), Tucotuco+Lemming (44), Ratifier+Zherolais+Rharolais+Bharolais (52), Fosterer+Frone (56), Boneshaker+Summing+Numming (76). Again to the short-range -leaper and long-range -rider suffix, are added -ROVER extending just the coprime component(s) -BANTE just the twice-coprime, et cetera.


Root-n-leapers where n is once, twice, or thrice an exact square are covered in MAB 19: The Vice Squad, as they mix radial components in with the oblique ones. The most complex hex-specific pieces have their own article, MAB 20: Far From Square.

Certain compounds cannot exist as no geometry has both pieces. These include Sexton+Prefect, Aurochs/Baker+Arbez, Mountie/Housemouse+Monk/Hogger, Offscore+Votary, Videoplayer+Viremaster, Goose/Cormorant/Bustard/Gull+Octodont, Barnowl+Bandicoot, Dancer+Dallier, Prizemouse/Woodmouse+Pipistrelle, Tesselator/Divider+Trembler, Epoletna+Anomalure, Drudge+Ducker, and Bettong+Beggar.

Galiot can also be spelled with a double L - galliot - but the single L distinguishes it more from other piece names starting with Gal- such as Galleon and Gallop.

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By Charles Gilman.
Web page created: 2008-08-09. Web page last updated: 2014-01-01